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Phase field modelling of fracture and fatigue in Shape Memory Alloys

Emilio Martínez Pañeda's picture

Dear iMechanicians. I hope that the following paper is of interest to you. We develop the first phase field formulation for fracture (and fatigue) in Shape Memory Alloys. Its potential is demonstrated by solving a variety of paradigmatic 2D and 3D boundary value problems, from R-curves to fatigue cracking of a NiTi biomedical stent.

M. Simoes, E. Martínez-Pañeda. Phase field modelling of fracture and fatigue in Shape Memory Alloys. Computer Methods in Applied Mechanics and Engineering 373 (2021) 113504


Phase field modelling of fracture and fatigue in Shape Memory Alloys

We present a new phase field framework for modelling fracture and fatigue in Shape Memory Alloys (SMAs). The constitutive model captures the superelastic behaviour of SMAs and damage is driven by the elastic and transformation strain energy densities. We consider both the assumption of a constant fracture energy and the case of a fracture energy dependent on the martensitic volume fraction. The framework is implemented in an implicit time integration scheme, with both monolithic and staggered solution strategies. The potential of this formulation is showcased by modelling a number of paradigmatic problems. First, a boundary layer model is used to examine crack tip fields and compute crack growth resistance curves (R-curves). We show that the model is able to capture the main fracture features associated with SMAs, including the toughening effect associated with stress-induced phase transformation. Insight is gained into the role of temperature, material strength, crack density function and fracture energy homogenisation. Secondly, several 2D and 3D boundary value problems are addressed, demonstrating the capabilities of the model in capturing complex cracking phenomena in SMAs, such as unstable crack growth, mixed-mode fracture or the interaction between several cracks. Finally, the model is extended to fatigue and used to capture crack nucleation and propagation in biomedical stents, a paradigmatic application of nitinol SMAs.

Contours of the phase field parameter  in the SMA stent during (compression–expansion) systolic–diastolic cycling.


cheikh cisse's picture

Nice work, but it looks more phenomenological with averaged internal variables than PFM with order parameters. 

Emilio Martínez Pañeda's picture

Dear Cheikh,

Thanks for your interest. The phase field method is used to model the cracking. It is a phase field fracture method. The martensite-austenite transformation is taken care of using averaged internal variables, as you say. One could use a two-field phase field approach but this is not the purpose of our work. Our aim was to present the first phase field formulation for fracture (and fatigue) in SMAs.

Emilio Martínez Pañeda

cheikh cisse's picture

Thank you Emilio for the answer. When I saw phase-field modeling which is known as a microscale method, I expected more details about the microstructure evolution such as the competition between the different martensite variants instead an averaged martensite at the macroscale.



Emilio Martínez Pañeda's picture

Thank you Cheikh for the clarification. In my view, the phase field method is a mathematical model, not pertaining to any scale. It is of course widely used in microstrutural evolution, as you say. But it is also very widely used in other interfacial problems at many differente scales. Fracture is one of them, where the phase field order parameter is used to differenciate between the cracked and solid parts of the material. Hope that this clarifies things.

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